how to construct min and max sum of products of permutations

Mon Jan 31 06:00:04 CET 2005

Diagrammatically:
odd case (let n be 7)
***    ***    ***   1 7
6 2   ***     ***   1 7
6 2   ***     3 5  1 7
6 2    4      3 5   1 7
even case (let n be 8)
  1    ***   ***   ***   ***   ***   ***    2
  1     3    ***   ***   ***    ***    4     2
  1     3     5     ***   ***     6     4     2
  1     3     5      7      8      6     4     2
And their reverses.